Introduction to Digital Filtering of an LPCM Signal and DAC Digital Filter Performance*

Artefacts from the sampling process, called folded tones, are removed during the process of increasing the sampling rate.

For a band-limited 20kHz analog signal sampled at a rate of 44.1kHz samples/sec (fs), the spectra appear around 0Hz (desired signal) as well as from 24.1kHz to 64.1kHz and then repeat around multiples of 44.1kHz. The repeating spectra are the stop-band images from the sampling process. For a 20kHz signal (fB), the right side of the first image (often called the folded frequency) is close-in at 22.1kHz (44.1kHz – 20kHz). The suppression of the stop-band images allows the sampled signal to better represent an analog signal sampled at 44.1kHz. Information lost from band limiting of the signal before the sampling process during recording cannot be restored, although some manufactures try to imply this. For high resolution files, fs will be between 88.2 – 192kHz. The maximum frequency that can be recorded (fB) can also be extended since the right side of the first image will be at a higher frequency.

The process of attenuating the stop-band images of a sampled signal takes place in the digital filters on the DAC, although these can be bypassed and replaced by external digital filters. To my knowledge, the only multichannel products to do this are from Cambridge Audio.

In general, DAC ICs with better SNR and THD specs devote more silicon to the filtering function. If the digital filter does not have a sufficiently low stopband rejection past half the sampling rate, the folded tones from the reconstruction process may dominate the harmonic distortion and noise spectra of the DAC when driven with a sine wave test tones. As the input frequency increases, the first folded tone frequencies move in the opposite direction. The performance of the digital filter is most significant under these conditions since the folded tones are moving towards half the sampling rate (22.1kHz for a CD). It is also possible for the folded tones to intermodulate with the harmonic distortion components giving rise to tones in the pass band.

The stopband rejection of the digital filter is increased by increasing the complexity of the filter. This involves increasing the order (number of zeros) to the filter. This increases the amount of silicon that must be devoted to the filter which increases the price of the DAC IC.

For the DACs at the top of an IC vendors line, with worst case THD, at full scale, ranging for -100dB to -110dB, the stopband attenuation will typically range from -100dB – 120dB below the unity gain. The stopband performance is specified in the datasheets found on the web for all but the ESS products.

It thus should come as no surprise that the parts with a lower performing analog section were the first to be made available as octal DACs. These parts also minimize the amount of silicon taken by the digital filter. This can be seen in a stopband rejection in the range of -55dB to -60dB.

For high resolution material, the folded tones are more widely spaced from the highest frequency of the desired signal. All DACs will achieve very high attenuation of folded tones for this reason.

A few data sheets for data converters and ASRCs, notably the ESS products, the number of bits in the data path or multiply-accumulate section of the digital signal processor are presented. The large number of extra bits, relative to the analog resolution of the DAC in effective bits, is required to prevent round off error in the computations. Digital filter coefficients must also be specified with extreme accuracy. While these numbers may be useful to estimate the passband and stopband characteristics of the digital filter, and it is far more useful, from the designer's standpoint, to look at the actual pass band and stop band characteristics of the digital filters. This is not supplied on the ESS public data sheets.

The passband frequency response also changes as the digital filter gets more complex. For the simplest filter found on the lowest priced DAC, the variation may be +/-0.1dB. For the very complex filter on the TI PCM 1972, the deviation is +/- 0.00001 dB. Mid-priced parts may be a couple orders less than this, but the digital filter passband frequency response is clearly dominated by the analog electronics.